One might already anticipate some parallelism of the DFT framework with generalized geometry,
in the sense that both formalisms are based on a doubled space.
However, an important difference is that in the former, what is doubled is the base manifold, while
in the latter is the tangent bundle.
This difference is important if one wants to understand T-duality in the generalized geometry setting,
since, as argued above, the very essence of T-duality is to exchange the manifolds \(T\)  and \(\tilde{T}\) .
Upon restriction to fields satisfying the strong constraint, the D-bracket reduces to the Dorfman bracket
and one can argue that the DFT setting reduces locally to generalized geometry (see e.g. [1]}).
A possible formalization of all this (that is also intended to provide a global formulation of DFT)
originates in the work of Vaisman in [2]}, [3]}, who
shows, in the first place, that the usual extended spacetime of DFT is a flat para-Kähler manifold.
To see this, consider first an almost para-Hermitian structure on a \(2d\) -dimensional manifold \(M\) :
a pair \((\eta ,K)\)  where \(K\in {\rm End}(TM)\)  and \(\eta \)  is a metric such that
\(K^{2}=\mathbb {I}, \qquad \eta (KX,KY)=-\eta (X,Y)\) 
